SOLUTION: The volume of the cube shown is 8 cubic centimeters. Cube image has (x-3)(x-3)(x-3) a. Write a polynomial equation that you can use to find the value of x. ? =0 b. don

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The volume of the cube shown is 8 cubic centimeters. Cube image has (x-3)(x-3)(x-3) a. Write a polynomial equation that you can use to find the value of x. ? =0 b. don      Log On


   

Question 1058687: The volume of the cube shown is 8 cubic centimeters.
Cube image has (x-3)(x-3)(x-3)
a. Write a polynomial equation that you can use to find the value of x.
? =0
b. done
c. Use synthetic division to find a rational solution of the equation. Show that no other real solutions exist.
Using synthetic division to divide by the factor results in a remainder of 0, so 5 is a solution.
The resulting equation ?=0
has solutions x=?
2 ±?, so there is only one real solution.
?= answers needed
Thank you!!!
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
(x-3)^3=(x-3)^2*(x-3)
(x^2-6x+9)(x-3)=x^3-3x^2-6x^2+18x+9x-27=
x^3-9x^2+27x-27=8
x^3-9x^2+27x-35=0
5/1===-9===27===-35
--1===-4===7====0
(x-5)(x^2-4x+7), the second has no real solutions. The discriminant, b^2-4ac=16-28=-12
x=5
the cube is 2*2*2
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3-9x%5E2%2B27x-35%29
a. x^3-9x^2+27x-35=0
c. 5/1===-9===27===-35
--1===-4===7====0
(x-5)(x^2-4x+7), the second has no real solutions. The discriminant, b^2-4ac=16-28=-12
Solutions: x=2, x=2+/-i*(sqrt(3)